Sensitivity of Weights in Combining Forecasts

In the combination of forecasts, weighted averages that attempt to take into account the accuracy of the forecasts and any dependence among forecasts tend to perform poorly in practice. An important factor influencing this performance is the sensitivity, or instability, of the estimated weights used to generate the combined forecast. The intent of this paper is to look at this instability via graphs and the sampling distribution of the weights. Results are developed for the combination of two forecasts and extended to the m-forecast case by viewing the m-forecast case as a sequence of two-forecast combinations.